There are many places that will host your web site for free. Even Internet access accounts from your ISP often come with free web site space. Free web site hosts may not offer all the services that your web site will need, or even allow you to use your own domain name. You should use a web site host that you trust, that provides the services that your web site needs at a cost that you are willing to pay. You will probably want to sign up for a website hosting account yourself to make sure that you have control of your website, but we will help if you want our help.
We don't host websites because hosting is a full time job, and we would rather design websites than maintain computers and chase away hackers. We recommend HostMonster to most of our customers. HostMonster is local (Utah) and I can call them whenever there is a problem. They are large enough that they have staff working 24/7 keeping their servers running. They are reasonably priced $6.95/month (usually they run a $5.95/month introductory pricing). They offer unlimited hosting space, unlimited bandwidth, unlimited domains in one account (for $10/domain), unlimited email addresses, and many website services. HostMonster pays us a small fee whenever we recommend customers but the main reason we like HostMonster is because we have many websites at HostMonster and we are familiar with the way they work. If you follow our link to HostMonster they will understand that we recommended you which benefits us.